If a and b are positive real numbers and a ∗ b denotes √(a × b), what is the value of 8 ∗ (4 ∗ 16)?

If x = ⁶√5 (sixth root of 5) and y = ⁵√4 (fifth root of 4), which of the following is true?

The average age of three men is 50 years and their ages are in the proportion 3:5:7. The age of the youngest man is:

In the figure, PQ is a diameter of the circle. Angle PQS = 35°. Find angle QRS. (R and S are points on the circle on opposite sides of PQ; chords RQ, RS and SQ are drawn.) [Figure: see page 6 of source PDF]

By selling mangoes at the rate of 64 for Rs. 2,000, the vendor loses 40%. How many should he sell for Rs. 1000 so as to gain 20%?

Number of different categories of goods sold in the city over the years (in thousands) is as given under: Year | TV | Refrigerator | Microwave | Laptops | Cell phones 2010 | 26 | 64 | 232 | 153 | 340 2011 | 45 | 60 | 242 | 172 | 336 2012 | 72 | 79 | 248 | 210 | 404 2013 | 81 | 93…

The area of a triangular metal plate with base 88 cm and altitude 64 cm is to be reduced to one-fourth of its original area by making a hole of circular shape at the center. The radius of this hole will be:

Expenditures of a company (in Lakh Rupees) per annum over the given years was as under. Year | Salary | Fuel and Transport | Bonus | Interest on loans | Taxes 2008 | 576 | 196 | 6 | 25.4 | 85 2009 | 682 | 224 | 5 | 32 | 112 2011 | 648 | 202 | 7.5 | 44.6 | 78 2012 | 672 | 266 | 7.…

Find the value of √[(2 + √3)/(2 − √3)], correct to three places of decimal.